HP 40gs Graphing Calculator User manual

HP 40gs graphing calculator

user's guide

Edition1

Part Number F2225AA-90001

hp40g+.book Page i Friday, December 9, 2005 1:03 AM

Notice

REGISTER YOUR PRODUCT AT: www.register.hp.com

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PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT

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FOR A PARTICULAR PURPOSE.

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ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES

IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR

USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.

opment Company, L.P.

Reproduction, adaptation, or translation of this manual is prohibited without

prior written permission of Hewlett-Packard Company, except as allowed

under the copyright laws.

Hewlett-Packard Company

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Suite 301

San Diego, CA 92123

Printing History

Edition 1 April 2005

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iii

Contents

Preface

Manual conventions .............................................................. P-1

Notice ................................................................................. P-2

1 Getting started

On/off, cancel operations......................................................1-1

The display ..........................................................................1-2

The keyboard .......................................................................1-3

Menus .................................................................................1-8

Input forms ...........................................................................1-9

Mode settings.....................................................................1-10

Setting a mode...............................................................1-11

Aplets (E-lessons).................................................................1-12

Aplet library ..................................................................1-16

Aplet views....................................................................1-16

Aplet view configuration..................................................1-18

Mathematical calculations....................................................1-19

Using fractions....................................................................1-25

Complex numbers ...............................................................1-29

Catalogs and editors ...........................................................1-30

2 Aplets and their views

Aplet views ..........................................................................2-1

About the Symbolic view ...................................................2-1

Defining an expression (Symbolic view) ..............................2-1

Evaluating expressions ......................................................2-3

About the Plot view...........................................................2-5

Setting up the plot (Plot view setup).....................................2-5

Exploring the graph..........................................................2-7

Other views for scaling and splitting the graph ..................2-13

About the numeric view...................................................2-16

Setting up the table (Numeric view setup) ..........................2-16

Exploring the table of numbers.........................................2-17

Building your own table of numbers..................................2-19

“Build Your Own” menu keys...........................................2-20

Example: plotting a circle ................................................2-20

3 Function aplet

About the Function aplet ........................................................3-1

Getting started with the Function aplet.................................3-1

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iv

Function aplet interactive analysis........................................... 3-9

Plotting a piecewise-defined function ................................ 3-12

4 Parametric aplet

About the Parametric aplet .................................................... 4-1

Getting started with the Parametric aplet............................. 4-1

5 Polar aplet

Getting started with the Polar aplet ......................................... 5-1

6 Sequence aplet

About the Sequence aplet...................................................... 6-1

Getting started with the Sequence aplet .............................. 6-1

7 Solve aplet

About the Solve aplet............................................................ 7-1

Getting started with the Solve aplet .................................... 7-2

Use an initial guess............................................................... 7-5

Interpreting results ................................................................ 7-6

Plotting to find guesses.......................................................... 7-7

Using variables in equations ................................................ 7-10

8 Linear Solver aplet

About the Linear Solver aplet ................................................. 8-1

Getting started with the Linear Solver aplet.......................... 8-1

9 Triangle Solve aplet

About the Triangle Solver aplet .............................................. 9-1

Getting started with the Triangle Solver aplet....................... 9-1

10 Statistics aplet

About the Statistics aplet...................................................... 10-1

Getting started with the Statistics aplet.............................. 10-1

Entering and editing statistical data ...................................... 10-6

Defining a regression model.......................................... 10-12

Computed statistics ........................................................... 10-14

Plotting............................................................................ 10-15

Plot types .................................................................... 10-16

Fitting a curve to 2VAR data ......................................... 10-17

Setting up the plot (Plot setup view) ................................ 10-18

Trouble-shooting a plot ................................................. 10-19

Exploring the graph ..................................................... 10-19

Calculating predicted values ......................................... 10-20

11 Inference aplet

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About the Inference aplet .....................................................11-1

Getting started with the Inference aplet .............................11-1

Importing sample statistics from the Statistics aplet ..............11-4

Hypothesis tests ..................................................................11-8

One-Sample Z-Test..........................................................11-8

Two-Sample Z-Test ..........................................................11-9

One-Proportion Z-Test....................................................11-10

Two-Proportion Z-Test ....................................................11-11

One-Sample T-Test ........................................................11-12

Two-Sample T-Test ........................................................11-14

Confidence intervals..........................................................11-15

One-Sample Z-Interval...................................................11-15

Two-Sample Z-Interval ...................................................11-16

One-Proportion Z-Interval...............................................11-17

Two-Proportion Z-Interval ...............................................11-17

One-Sample T-Interval ...................................................11-18

Two-Sample T-Interval....................................................11-19

12 Using the Finance Solver

Background........................................................................12-1

Performing TVM calculations ................................................12-4

Calculating Amortizations................................................12-7

13 Using mathematical functions

Math functions....................................................................13-1

The MATH menu ............................................................13-1

Math functions by category ..................................................13-2

Keyboard functions.........................................................13-3

Calculus functions...........................................................13-6

Complex number functions...............................................13-7

Constants ......................................................................13-8

Conversions...................................................................13-8

Hyperbolic trigonometry..................................................13-9

List functions ................................................................13-10

Loop functions..............................................................13-10

Matrix functions ...........................................................13-11

Polynomial functions .....................................................13-11

Probability functions......................................................13-12

Real-number functions ...................................................13-14

Two-variable statistics....................................................13-17

Symbolic functions........................................................13-17

Test functions ...............................................................13-19

Trigonometry functions ..................................................13-20

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vi

Symbolic calculations........................................................ 13-20

Finding derivatives....................................................... 13-21

Program constants and physical constants ........................... 13-24

Program constants........................................................ 13-25

Physical constants ........................................................ 13-25

14 Computer Algebra System (CAS)

What is a CAS? ................................................................. 14-1

Performing symbolic calculations .......................................... 14-1

An example .................................................................. 14-2

CAS variables.................................................................... 14-4

The current variable ....................................................... 14-4

CAS modes ....................................................................... 14-5

Using CAS functions in HOME............................................. 14-7

Online Help....................................................................... 14-8

CAS functions in the Equation Writer .................................... 14-9

ALGB menu................................................................. 14-10

DIFF menu................................................................... 14-16

REWRI menu ............................................................... 14-28

SOLV menu................................................................. 14-33

TRIG menu .................................................................. 14-38

CAS Functions on the MATH menu ..................................... 14-45

Algebra menu ............................................................. 14-45

Complex menu ............................................................ 14-45

Constant menu ............................................................ 14-46

Diff & Int menu ............................................................ 14-46

Hyperb menu .............................................................. 14-46

Integer menu ............................................................... 14-46

Modular menu............................................................. 14-51

Polynomial menu ......................................................... 14-55

Real menu................................................................... 14-60

Rewrite menu .............................................................. 14-60

Solve menu ................................................................. 14-60

Tests menu .................................................................. 14-61

Trig menu ................................................................... 14-61

CAS Functions on the CMDS menu ..................................... 14-62

15 Equation Writer

Using CAS in the Equation Writer ....................................... 15-1

The Equation Writer menu bar......................................... 15-1

Configuration menus ...................................................... 15-3

Entering expressions and subexpressions............................... 15-5

How to modify an expression ....................................... 15-11

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vii

Accessing CAS functions....................................................15-12

Equation Writer variables .................................................15-16

Predefined CAS variables .............................................15-16

The keyboard in the Equation Writer ..............................15-17

16 Step-by-Step Examples

Introduction .......................................................................16-1

17 Variables and memory management

Introduction ........................................................................17-1

Storing and recalling variables .............................................17-2

The VARS menu ..................................................................17-4

Memory Manager...............................................................17-9

18 Matrices

Introduction ........................................................................18-1

Creating and storing matrices...............................................18-2

Working with matrices.........................................................18-4

Matrix arithmetic.................................................................18-6

Solving systems of linear equations...................................18-8

Matrix functions and commands..........................................18-10

Argument conventions...................................................18-10

Matrix functions ...........................................................18-10

Examples .........................................................................18-13

19 Lists

Displaying and editing lists...................................................19-4

Deleting lists ..................................................................19-6

Transmitting lists .............................................................19-6

List functions .......................................................................19-6

Finding statistical values for list elements ................................19-9

20 Notes and sketches

Introduction ........................................................................20-1

Aplet note view...................................................................20-1

Aplet sketch view ................................................................20-3

The notepad.......................................................................20-6

21 Programming

Introduction ........................................................................21-1

Program catalog ............................................................21-2

Creating and editing programs.............................................21-4

Using programs ..................................................................21-7

Customizing an aplet...........................................................21-9

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Aplet naming convention .............................................. 21-10

Example ..................................................................... 21-10

Programming commands ................................................... 21-13

Aplet commands.......................................................... 21-14

Branch commands ....................................................... 21-17

Drawing commands ..................................................... 21-19

Graphic commands...................................................... 21-21

Loop commands .......................................................... 21-23

Matrix commands ........................................................ 21-24

Print commands ........................................................... 21-25

Prompt commands........................................................ 21-26

Stat-One and Stat-Two commands.................................. 21-29

Stat-Two commands ..................................................... 21-30

Storing and retrieving variables in programs ................... 21-31

Plot-view variables ....................................................... 21-31

Symbolic-view variables................................................ 21-38

Numeric-view variables ................................................ 21-40

Note variables............................................................. 21-43

Sketch variables .......................................................... 21-43

22 Extending aplets

Creating new aplets based on existing aplets......................... 22-1

Using a customized aplet................................................ 22-3

Resetting an aplet ............................................................... 22-3

Annotating an aplet with notes............................................. 22-4

Annotating an aplet with sketches......................................... 22-4

Downloading e-lessons from the web .................................... 22-4

Sending and receiving aplets............................................... 22-4

Sorting items in the aplet library menu list.............................. 22-6

Reference information

Glossary.............................................................................. R-1

Resetting the HP 40gs ........................................................... R-3

To erase all memory and reset defaults............................... R-3

If the calculator does not turn on........................................ R-4

Operating details ................................................................. R-4

Batteries ......................................................................... R-4

Variables............................................................................. R-6

Home variables ............................................................... R-6

Function aplet variables.................................................... R-7

Parametric aplet variables................................................. R-8

Polar aplet variables ........................................................ R-9

Sequence aplet variables................................................ R-10

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ix

Solve aplet variables.......................................................R-11

Statistics aplet variables ..................................................R-12

MATH menu categories .......................................................R-13

Math functions ...............................................................R-13

Program constants ..........................................................R-15

Physical Constants ..........................................................R-16

CAS functions ................................................................R-17

Program commands........................................................R-19

Status messages..................................................................R-20

Limited Warranty

Service.......................................................................... W-3

Regulatory Notices ......................................................... W-5

Index

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P-1

Preface

The HP 40gs is a feature-rich graphing calculator. It is

also a powerful mathematics learning tool, with a built-in

computer algebra system (CAS). The HP 40gs is designed

so that you can use it to explore mathematical functions

and their properties.

You can get more information on the HP 40gs from

Hewlett-Packard’s Calculators web site. You can

download customized aplets from the web site and load

them onto your calculator. Customized aplets are special

applications developed to perform certain functions, and

to demonstrate mathematical concepts.

Hewlett Packard’s Calculators web site can be found at:

http://www.hp.com/calculators

Manual conventions

The following conventions are used in this manual to

represent the keys that you press and the menu options

that you choose to perform the described operations.

• Key presses are represented as follows:

, , , etc.

• Shift keys, that is the key functions that you access by

pressing the key first, are represented as

follows:

CLEAR, MODES, ACOS, etc.

• Numbers and letters are represented normally, as

follows:

5, 7, A, B, etc.

• Menu options, that is, the functions that you select

using the menu keys at the top of the keypad are

represented as follows:

, , .

• Input form fields and choose list items are represented

as follows:

Function, Polar, Parametric

• Your entries as they appear on the command line or

within input forms are represented as follows:

2*X

2

-3X+5

hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM

P-2

Notice

This manual and any examples contained herein are

provided as-is and are subject to change without notice.

Except to the extent prohibited by law, Hewlett-Packard

Company makes no express or implied warranty of any

kind with regard to this manual and specifically disclaims

the implied warranties and conditions of merchantability

and fitness for a particular purpose and Hewlett-Packard

Company shall not be liable for any errors or for

incidental or consequential damage in connection with

the furnishing, performance or use of this manual and the

examples herein.

©

Hewlett-Packard Development Company, L.P.

The programs that control your HP 40gs are copyrighted

and all rights are reserved. Reproduction, adaptation, or

translation of those programs without prior written

permission from Hewlett-Packard Company is also

prohibited.

Preface.fm Page 2 Friday, February 17, 2006 9:47 AM

Getting started 1-1

1

Getting started

On/off, cancel operations

To turn on Press to turn on the calculator.

To cancel When the calculator is on, the key cancels the

current operation.

To turn off Press OFF to turn the calculator off.

To save power, the calculator turns itself off after several

minutes of inactivity. All stored and displayed information

is saved.

If you see the ((•)) annunciator or the Low Bat message,

then the calculator needs fresh batteries.

HOME HOME is the calculator’s home view and is common to all

aplets. If you want to perform calculations, or you want to

quit the current activity (such as an aplet, a program, or

an editor), press . All mathematical functions are

available in the HOME. The name of the current aplet is

displayed in the title of the home view.

Protective cover The calculator is provided with a slide cover to protect the

display and keyboard. Remove the cover by grasping

both sides of it and pulling down.

You can reverse the slide cover and slide it onto the back

of the calculator. this will help prevent you losing the

cover while you are using the calculator.

To prolong the life of the calculator, always place the

cover over the display and keyboard when you are not

using the calculator.

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1-2 Getting started

The display

To adjust the

contrast

Simultaneously press and (or ) to increase (or

decrease) the contrast.

To clear the display • Press CANCEL to clear the edit line.

• Press

CLEAR to clear the edit line and the

display history.

Parts of the

display

Menu key or soft key labels. The labels for the menu

keys’ current meanings. is the label for the first

menu key in this picture. “Press ” means to press the

first menu key, that is, the leftmost top-row key on the

calculator keyboard.

Edit line. The line of current entry.

History. The HOME display ( ) shows up to four

lines of history: the most recent input and output. Older

lines scroll off the top of the display but are retained in

memory.

Title. The name of the current aplet is displayed at the top

of the HOME view. RAD, GRD, DEG specify whether

Radians, Grads or Degrees angle mode is set for HOME.

The

T and S symbols indicate whether there is more

history in the HOME display. Press the and to

scroll in the HOME display.

Title

Edit line

History

Menu key

labels

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Getting started 1-3

Annunciators. Annunciators are symbols that appear

above the title bar and give you important status

information.

The keyboard

Annunciator Description

Shift in effect for next keystroke.

To cancel, press again.

α Alpha in effect for next keystroke.

To cancel, press again.

((•)) Low battery power.

Busy.

Data is being transferred.

Menu Key

Labels

Menu Keys

Cursor

Aplet Control

Alpha Key

Shift Key

Enter

Keys

Key

Keys

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1-4 Getting started

Menu keys

• On the calculator keyboard, the top row of keys are

called menu keys. Their meanings depend on the

context—that’s why they are blank. The menu keys

are sometimes called “soft keys”.

• The bottom line of the display shows the labels for the

menu keys’ current meanings.

Aplet control keys

The aplet control keys are:

Key Meaning

Displays the Symbolic view for the

current aplet. See “Symbolic view”

on page 1-16.

Displays the Plot view for the current

aplet. See “Plot view” on page 1-16.

Displays the Numeric view for the

current aplet. See “Numeric view” on

page 1-17.

Displays the HOME view. See

“HOME” on page 1-1.

Displays the Aplet Library menu. See

“Aplet library” on page 1-16.

Displays the VIEWS menu. See

“Aplet views” on page 1-16.

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Getting started 1-5

Entry/Edit keys

The entry and edit keys are:

Key Meaning

(

CANCEL)

Cancels the current operation if the

calculator is on by pressing .

Pressing , then

OFF turns the

calculator off.

Accesses the function printed in blue

above a key.

Returns to the HOME view, for

performing calculations.

Accesses the alphabetical

characters printed in orange below

a key. Hold down to enter a string

of characters.

Enters an input or executes an

operation. In calculations,

acts like “=”. When or

is present as a menu key,

acts the same as pressing or

.

Enters a negative number. To enter

–25, press 25. Note: this is not

the same operation that the subtract

button performs ().

Enters the independent variable by

inserting X, T, θ, or N into the edit

line, depending on the current

active aplet.

Deletes the character under the

cursor. Acts as a backspace key if

the cursor is at the end of the line.

CLEAR

Clears all data on the screen. On a

settings screen, for example Plot

Setup, CLEAR returns all

settings to their default values.

, , ,

Moves the cursor around the

display. Press first to move to

the beginning, end, top or bottom.

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1-6 Getting started

Shifted keystrokes

There are two shift keys that you use to access the

operations and characters printed above the keys:

and .

CHARS Displays a menu of all available

characters. To type one, use the

arrow keys to highlight it, and press

. To select multiple characters,

select each and press , then

press .

Key Meaning (Continued)

Key Description

Press the key to access the

operations printed in blue above the

keys. For instance, to access the

Modes screen, press , then

press . (MODES is labeled in

blue above the key). You do

not need to hold down when

you press HOME. This action is

depicted in this manual as “press

MODES.”

To cancel a shift, press again.

The alphabetic keys are also shifted

keystrokes. For instance, to type Z,

press Z. (The letters are

printed in orange to the lower right of

each key.)

To cancel Alpha, press

again.

For a lower case letter, press

.

For a string of letters, hold down

while typing.

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Getting started 1-7

HELPWITH The HP 40gs built-in help is available in HOME only. It

provides syntax help for built-in math functions.

Access the HELPWITH command by pressing

SYNTAX and then the math key for which you require

syntax help.

Example Press SYNTAX

Note: Remove the left parenthesis from built-in

functions such as sine, cosine, and tangent before

invoking the HELPWITH command.

Note: In the CAS system, pressing the SYNTAX

will show the CAS help menu.

Math keys HOME ( ) is the place to do non-symbolic

calculations. (For symbolic calculations, use the computer

algebra system, referred throughout this manual as CAS).

Keyboard keys. The most common operations are

available from the keyboard, such as the arithmetic (like

) and trigonometric (like ) functions. Press

to complete the operation: 256

displays 16.

.

MATH menu. Press

to open the MATH

menu. The MATH menu is a

comprehensive list of math

functions that do not appear

on the keyboard. It also

includes categories for all other functions and constants.

The functions are grouped by category, ranging in

alphabetical order from Calculus to Trigonometry.

• The arrow keys scroll through the list ( , )

and move from the category list in the left column

to the item list in the right column ( , ).

• Press to insert the selected command onto the

edit line.

• Press to dismiss the MATH menu without

selecting a command.

chapter-1.fm Page 7 Friday, December 16, 2005 2:20 PM

1-8 Getting started

• Pressing displays the list of Program

Constants. You can use these in programs that

you develop.

• Pressing displays a menu of physical

constants from the fields of chemistry, physics,

and quantum mechanics. You can use these

constants in calculations. (pSee “Physical

constants” on page 13-25 for more information.)

• Pressing takes you to the beginning of the

MATH menu.

See “Math functions by category” on page 13-2 for

details of the math functions.

HINT

When using the MATH menu, or any menu on the

HP 40gs, pressing an alpha key takes you straight to the

first menu option beginning with that alpha character.

With this method, you do not need to press first.

Just press the key that corresponds to the command’s

beginning alpha character.

Note that when the MATH menu is open, you can also

access CAS commands. You do this by pressing .

This enables you to use CAS commands on the HOME

screen, without opening CAS. See Chapter 14 for details

of CAS commands.

Program

commands

Pressing CMDS displays the list of Program

Commands. See “Programming commands” on

page 21-13.

Inactive keys If you press a key that does not operate in the current

context, a warning symbol like this appears. There is

no beep.

Menus

A menu offers you a choice

of items. Menus are

displayed in one or two

columns.

• The arrow in the

display means more

items below.

• The arrow in the

display means more items above.

!

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